Cosmic-Ray Muon Integral Intensity Measurement Under Water

The cosmic-ray muon integral intensity ($E_{\mu -\mathrm{threshold}}\gtrsim 1\frac{\mathrm{GeV}}{c}$) was measured under water with a detector of small angular aperture (6.5° full width at half maximum). The motivation of the work was to check the range-energy relation for muons under a medium, water, whose properties are very well known and whose atomic properties ($Z,\frac{Z^2}{A}$) are significantly different from "rock" used in underground measurements. The ratio of these measured relative muon intensities, converted to equivalent depths of standard rock, to those measured under rock and converted to standard rock, for 50 hg ${\mathrm{cm}}^{-2\mathrm{}}$ $\lesssim d\lesssim$ 1000 hg ${\mathrm{cm}}^{-2\mathrm{}}$ of equivalent standard rock, is 1.09± 0.06. This measurement shows that the range-energy interactions of muons are consistent between "rock" and water for $E_{\mu }\lesssim 240$ GeV.